# Comparison of two linear regression models with squared regressors

I need to compare two linear regression models that include the regressors in levels and in squares:

$Y=a_1x^2+b_1x+c_1$ and $Y=a_2x^2+b_2x+c_2$

Specifically, I need to test whether these regression models are significantly different (i.e., whether $a_1=a_2,b_1=b_2,c_1=c_2$).

In the forum, I read that one should build respective interactions.

Yet, I do not exactly understand what is meant by including “interactions.”

What would that model look like? What should be compared with what, and what test statistic is best?

(I do not know Stata, unfortunately.)

Your 2 models have the same regressors but different coefficients. The easiest thing to do is to check the confidence intervals for overlapping. For example, if CI of $a_1$ overlaps CI of $a_2$ or covers $a_2$ if only one model is fit, then there is no significant difference between them. You can do this for all 3 coefficients.